Revealing network topology and dynamical parameters in delay-coupled complex network subjected to random noise

Abstract

It is well known that random noise and time delay are two inherent ingredients in complex networks, whose dynamical parameters and topological structures are often unknown or uncertain. This paper will employ the techniques of impulsive control and adaptive control to infer dynamical parameters and network topology in delay-coupled complex network under circumstance noise. By constructing an appropriate adaptive–impulsive control strategy in the response network, the unknown dynamical parameters and topology structure contained in the drive network are to be accurately identified; moreover, these two networks will achieve the global exponential synchronization in mean square. Based on the comparison theorem of impulsive differential equations, the accuracy of the proposed identification strategy is rigorously proved. Finally, two examples with networks of chaotic oscillators are presented to illustrate the application of the suggested strategy. Meanwhile, numerical results indicate that our proposed scheme is robust against the impulsive gain, the update gain and the network topology.